Modeling and Analysis of Mood Dynamics in the Bipolar Spectrum

Abstract

This article introduces a nonlinear ordinary differential equation model of mood dynamics for disorders on the bipolar spectrum. Motivated by biopsychosocial findings, the model characterizes mood as a 2-D state corresponding to manic and depressive features, enabling the representation of most diagnoses of bipolar and depressive disorders. We perform a mathematical analysis of conditions for the mood to stabilize to euthymia and discuss its psychotherapeutic implications. Furthermore, a computational analysis applied to pharmacotherapy depicts a mechanism that results in a switch from depression to mania when the bipolar disorder was misdiagnosed as major depressive disorder, and an antidepressant is administered without a mood stabilizer. This work innovates by offering a concise representation of most features of mood disorders in existing mathematical models, providing a framework for studying dynamics in the bipolar spectrum.